Abstract: Density is one of the most important physical properties of the object, because it can determine the total mass, center of mass and moment of inertia of the model. In order to implement the center of mass modelling of 3D printed objects with a single material, this paper proposed an internal supporting structure modeling method based on aware density. First, a mesh offset operation is conducted, which is based on implicit surface modeling method and then the voxelization algorithm is used to divide the geometric space. Next, the objective function and the constraint conditions are constructed, and solved. Last, the controllable porous structure with the implicit function is used to realize the density modeling of the spatial domain. Experimental results show that the method can generate the model with gradient and smooth porous structures which can meet the center of mass property.